feat: add ConstrainNotEqual instruction

[TomAFrench]

Description

Problem*

Resolves

Summary*

Currently when asserting that two values are not equal we need to use

v2 = eq v0, v1
constrain v2 == u1 0

Because we have a full eq instruction being passed to acirgen we need all the handling for the case where the two values ARE equal. Rather than just asserting that an inverse exists for the difference between these two values we need to create two unnecessary witnesses - one which is unconstrained and the other constrained to zedo. This is unnecessary as we want the circuit to just fail in this case.

This PR creates a ConstrainNotEqual instruction that allows ACIRgen to just directly assert that an inverse exists.

Additional Context

Documentation*

Check one:

• No documentation needed.
• Documentation included in this PR.
• [For Experimental Features] Documentation to be submitted in a separate PR.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[github-actions]

Execution Report

Program	Execution Time	%
sha256_regression	0.052s	1%
regression_4709	0.001s	0%
ram_blowup_regression	0.625s	2%
rollup-root	0.103s	-1%
rollup-merge	0.006s	-15%
rollup-block-root	36.900s	1%
rollup-block-merge	0.104s	-1%
rollup-base-public	1.223s	1%
rollup-base-private	0.449s	-1%
private-kernel-tail	0.019s	0%
private-kernel-reset	0.311s	0%
private-kernel-inner	0.067s	-2%

[github-actions]

Compilation Report

Program	Compilation Time	%
sha256_regression	1.100s	-5%
regression_4709	0.861s	-10%
ram_blowup_regression	16.300s	-2%
rollup-root	3.554s	1%
rollup-merge	2.064s	-3%
rollup-block-root-single-tx	136.000s	-2%
rollup-block-root-empty	2.054s	-2%
rollup-block-root	138.000s	-1%
rollup-block-merge	3.690s	4%
rollup-base-public	28.020s	0%
rollup-base-private	10.154s	-4%
private-kernel-tail	0.956s	-2%
private-kernel-reset	6.158s	-5%
private-kernel-inner	1.938s	-5%

[github-actions]

Compilation Memory Report

Program	Peak Memory
keccak256	77.65M
workspace	123.82M
regression_4709	424.15M
ram_blowup_regression	1.46G
rollup-root	601.04M
rollup-merge	494.01M
rollup-block-root-single-tx	16.06G
rollup-block-root-empty	488.18M
rollup-block-root	16.07G
rollup-block-merge	601.03M
rollup-base-public	2.38G
rollup-base-private	1.14G
private-kernel-tail	207.27M
private-kernel-reset	584.29M
private-kernel-inner	294.48M

[github-actions]

Execution Memory Report

Program	Peak Memory
keccak256	74.71M
workspace	124.00M
regression_4709	316.02M
ram_blowup_regression	512.62M
rollup-root	498.39M
rollup-merge	473.13M
rollup-block-root	1.22G
rollup-block-merge	498.40M
rollup-base-public	733.92M
rollup-base-private	590.58M
private-kernel-tail	180.71M
private-kernel-reset	245.32M
private-kernel-inner	208.72M

[github-actions]

Changes to circuit sizes

Generated at commit: a50494ab30470cb91f7c3fc85943a8c5097b70d8, compared to commit: 48e613ea97afb829012b3c5b1f8181d4f5ccfb7b

🧾 Summary (10% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
inline_never_basic	-3 ✅	-60.00%	-2 ✅	-10.00%
modules	-3 ✅	-60.00%	-2 ✅	-10.00%
modules_more	-3 ✅	-60.00%	-2 ✅	-10.00%
no_predicates_basic	-3 ✅	-60.00%	-2 ✅	-10.00%
type_aliases	-2 ✅	-40.00%	-2 ✅	-10.00%
regression_6451	-6 ✅	-42.86%	-4 ✅	-14.81%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
array_dynamic	97 (-3)	-3.00%	3,718 (0)	0.00%
bench_eddsa_poseidon	16,439 (+1)	+0.01%	19,585 (0)	0.00%
bench_2_to_17	6,534 (-2)	-0.03%	130,733 (-2)	-0.00%
conditional_regression_short_circuit	365 (-2)	-0.54%	11,137 (-2)	-0.02%
conditional_1	2,858 (-2)	-0.07%	10,287 (-2)	-0.02%
binary_operator_overloading	119 (-3)	-2.46%	4,260 (-2)	-0.05%
pedersen_check	19 (-3)	-13.64%	3,172 (-2)	-0.06%
xor	5 (-2)	-28.57%	3,144 (-2)	-0.06%
global_var_regression_simple	127 (-3)	-2.31%	3,066 (-2)	-0.07%
regression_4709	66 (-3)	-4.35%	2,914 (-2)	-0.07%
struct_inputs	25 (-3)	-10.71%	2,831 (-2)	-0.07%
regression_3607	36 (-2)	-5.26%	2,797 (-2)	-0.07%
array_to_slice	61 (-3)	-4.69%	287 (-2)	-0.69%
6_array	317 (-75)	-19.13%	3,981 (-50)	-1.24%
array_sort	49 (-4)	-7.55%	124 (-4)	-3.13%
main_bool_arg	5 (-3)	-37.50%	21 (-2)	-8.70%
import	4 (-3)	-42.86%	19 (-2)	-9.52%
witness_compression	3 (-3)	-50.00%	19 (-2)	-9.52%
inline_never_basic	2 (-3)	-60.00%	18 (-2)	-10.00%
modules	2 (-3)	-60.00%	18 (-2)	-10.00%
modules_more	2 (-3)	-60.00%	18 (-2)	-10.00%
no_predicates_basic	2 (-3)	-60.00%	18 (-2)	-10.00%
type_aliases	3 (-2)	-40.00%	18 (-2)	-10.00%
regression_6451	8 (-6)	-42.86%	23 (-4)	-14.81%

[aakoshh]

👍